Data Science different topic's explanation -- Part-8 -- Continuous distributions

[anish-arya]

This is data science different topic explanation conversation series.
If you are not following below mentioned are the links for each part.

Part-1:

Data Science different explanation -- An introduction

Data Science different explanation – An introduction [image] There are a lot of engineers who have never been involved in the field of statistics or Data Science. But in order to build data pipelines or rewrite produced code by Data Scientists to an adequate, easily maintained code many nuances and misunderstandings arise on the engineering side. For those Data/ML engineers and novice Data Scientists, I’ve made this series of posts. I will try to explain some basic approaches in plain eng…

Part-2:

Data Science different topic explanation -- Part-2 -- Events. Probabilities of events

If you missed the previous post, here’s the below mentioned link. Data Science different topic explanation – Part-2 – Events. Probabilities of events One of the basic concepts in statistics in an event. Events are simply results of experiments. Events can be certain impossible, or random. A certain event is an event that as a result of an experiment (the execution of certain actions with a certain set of conditions) will occur in 100% cases. For instance, tossed coin will certainly fall (on…

Part-3:

Data Science different topic explanation -- Part-3 -- Event Types

Continue above post. Example: What are the chances of getting heads 3 times in a row? Let’s define possible outcomes of 3 coin tosses (H-Heads, T-tails): HHH, HHT, HTH, THH, TTH HTH, HTT, TTT Number of ways it can happen: 1 Total number of outcomes: 8 So, the answer is 1/8. However, we know that the results of a coin toss are independent and we can multiply them to get the total probability: P(3x heads) = P(heads)P(heads)P(heads) = 1/2 * 1/2 * 1/2 = 1/8 On the other hand, knowing that the…

Part-4:

Data Science different topic explanation -- Part-4 -- Disjoint and overlapping events

This is data science different topic explanation conversation series. If you are not following below mentioned are the links for each part. Part-1: Part-2: Part-3: Data Science different topic explanation – Part-4 – Disjoint and overlapping events Disjoint events cannot happen at the same time. A synonym for this term is “mutually exclusive”. For instance, the outcome of a single coin toss cannot be head and a tail, it can be either head or tails. The not disjoint event can happend a…

Part-5:

Data Science different topic's explanation -- Part-5 -- Types of Probabilities

This is data science different topic explanation conversation series. If you are not following below mentioned are the links for each part. Part-1: Part-2: Part-3: Part-4: Data Science different topic’s explanation – Part-5 – Types of Probabilities Joint Probability Joint probability is a type of probability where more than one event can occur simultaneously. The joint probability is the probability that event A will occur at the same time as event B. For instance, from a deck o…

Part-6:

Data Science different topic's explanation -- Part-6 -- Marginal Probability and Conditional Probability

This is data science different topic explanation conversation series. If you are not following below mentioned are the links for each part. Part-1: Part-2: Part-3: Part-4: Part-5: Data Science different topic’s explanation – Part-6 – Marginal Probability and Conditional Probability Marginal Probability Marginal Probability – a probability of any single event occurring unconditioned on any other events. Whenever someone asks you whether the weather is going to be rainy or sunny t…

Part-7:

Data Science different topic's explanation -- Part-7 -- Probability Distributions

This is data science different topic explanation conversation series. If you are not following below mentioned are the links for each part. Part-1: Part-2: Part-3: Part-4: Part-5: Part-6: Data Science different topic’s explanation – Part-7 – Probability Distributions There are a lot of engineers who have never been involved in the field of statistics or data science. But in order to build data science pipelines or rewrite produced code by data scientists to an adequate, easily ma…

Continuous distributions

We investigate probabilistic distributions of continuous random variables, i.e. random variables whose support contains an infinite range of possible outcomes.

Uniform Distribution

A uniform distribution is a type of distribution of probabilities where all outcomes are equally likely; each variable has the same probability that it will be the outcome. A deck of cards has within tis uniform distributions because the probability that a heart, club, diamond, or spade is pulled is the same. The coin also has a uniform distribution because the probability of either the head or the tail in the coin toss is the same.

from scipy.stats import uniform
import matplotlib.pyplot as plt
import numpy as np


def uniform() -> None:
    fig, ax = plt.subplots(1, 1, figsize=(15,15))
    # calculate a few first moments
    mean, var, skew, kurt = uniform.stats(moments='mvsk')
    # display the probability density function (`pdf`)
    x = np.linspace(uniform.ppf(0.01), uniform.ppf(0.99), 100)
    ax.plot(x, uniform.pdf(x),
        'r-', lw=5, alpha=0.6, label='uniform pdf')
    ax.plot(x, uniform.cdf(x),
        'b-', lw=5, alpha=0.6, label='uniform cdf')
    # Check accuracy of `cdf` and `ppf`
    vals = uniform.ppf([0.001, 0.5, 0.999])
    np.allclose([0.001, 0.5, 0.999], uniform.cdf(vals))

    # generate random numbers
    r = uniform.rvs(size=1000)
    # and compare the histogram
    ax.hist(r, normed=True, histtype='stepfilled', alpha=0.2)
    ax.legend(loc='best', frameon=False)
    plt.show()

uniform() 

Make sure give this post a like for support and motivation for fresh content.

[anish-arya]

Continuing the left over content here for above post.

More formally this is the distribution of a random variable that can take any value in the interval (a,b) and the probability of being in any segment inside (a,b) is proportional to the length of the segment and does not depend on its position, and the probability of values outside the interval (a,b) is equal to 0.

So, a continuous random variable x has a uniform distribution, denoted U(a,b) if its probability density function is: